Non-trivial phase conjecture for RFP MPDOs from the Lee-Yang C*-weak Hopf algebra

Let the Lee-Yang C*-weak Hopf algebra be the algebra described in Example~, and let the associated RFP MPDOs be the renormalization fixed-point matrix product density operators constructed from it. The phase classification for RFP MPDOs from general biconnected C*-weak Hopf algebras is an open problem. Lee-Yang non-trivial-phase conjecture. RFP MPDOs arising from the Lee-Yang C*-weak Hopf algebra do not belong to the trivial phase. This is concrete evidence for the existence of non-trivial phases beyond the C*-Hopf-algebra case, where the paper proves that the corresponding RFP MPDOs belong to the trivial phase.